Polarization mode dispersion compensator based on degree of polarization

ABSTRACT

The degree of polarization of an optical signal is measured by a polarimeter and used for providing a feedback signal to adjust adaptive optics of a polarization mode dispersion compensator. The polarization properties of the polarimeter are determined with high accuracy to match the polarimeter through calibration and used to produce the feedback signal.

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application is a continuation application of InternationalPCT Application No. PCT/JP01/07568 which was filed on Aug. 31, 2001.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to a polarization mode dispersioncompensator for analyzing signal distortion due to polarization modedispersion in optical transmission systems and therefore providing afeedback signal to adjust adaptive optics used for mitigatingpolarization mode dispersion.

[0004] 2. Description of the Related Art

[0005] The higher the bit rate of an optical transmission system, themore a specific amount of polarization mode dispersion of an opticalfiber distorts the transmitted signal.

[0006] Due to polarization mode dispersion, the two modes in a so calledsingle-mode fiber propagate with different velocities. An initial pulsesplits its energy into the two modes. The two modes experience adifferential delay during propagation. This leads to pulse spreading atthe end of the fiber. The more the differential delay between the twomodes is in the order of the bit duration, the more neighboring pulseswill overlap, which leads at least to an increasing bit-error rate ormakes it even impossible to differentiate the pulses. Polarization modedispersion is due to internal birefringence (e.g. fiber core geometryirregularities) or externally induced birefringence (e.g. bending,squeezing, etc.). Because in a long single-mode fiber, polarization modecoupling occurs at randomly varying locations with randomly fluctuatingstrength due to e.g. environmental changes like temperature,polarization mode dispersion itself varies over time. It is well known,that the instantaneous differential group delay between the principalstates of polarization follows a Maxwellian probability densityfunction. The mean of the Maxwellian distributed instantaneousdifferential group delay is known as the average differential groupdelay, or the polarization mode dispersion value (PMD) of the fiber. Thepolarization mode dispersion value is, for long single-mode fibers withhigh polarization mode coupling, proportional to the square root of thefiber length.

[0007] To mitigate signal distortion due to polarization modedispersion, optical elements introducing a similar amount ofdifferential group delay as in the fiber but with an opposite sign, canbe placed at the end of the fiber. Due to the random nature of theinstantaneous differential group delay and the principal states ofpolarization in a long optical fiber, the optical elements used forcompensating polarization mode dispersion must be adaptively adjusted tothe momentary fiber conditions. A closed loop design, polarization modedispersion compensator consequently consists of:

[0008] 1. adaptively adjustable optical elements (adaptive optics)

[0009] 2. distortion analyzer

[0010] 3. control logic

[0011] as depicted in FIG. 1.

[0012] In FIG. 1, the distortion analyzer 12 provides a measure ofsignal distortion for the control logic 13 to adaptively adjust theadaptive optics 11, such that they best match the momentary polarizationmode dispersion conditions of the optical fiber.

[0013] Beside methods like for example spectral hole burning (SHB),direct eye-opening analyzing, etc., the degree of polarization (DOP) canbe used for analyzing signal distortion due to polarization modedispersion. For those who are skilled in the art, it is well known thata light beam experiences depolarization if the coherence length, whichis inversely proportional to the spectral width, is in the order of thedifferential group delay. The higher the differential group delaybecomes compared to the coherence length, the more the beam getsdepolarized and its degree of polarization decreases. This well knownphysical effect is straightforward to be used as a feedback signal toadaptively control optical elements of a polarization mode dispersioncompensator. Derivation of the depolarization of an optical signal dueto fiber anisotropies as a function of signal spectrum (bandwidth,form), differential group delay and state of input polarization is shownin the following reference.

[0014] “Degree of Polarization in Anisotropic Single-Mode OpticalFibers: Theory”, Jun-ichi Sakai, SusumuMachida, Tatsuya Kimura, IEEEJournal of Quantum Electronics, Vol. QE-18, No. 4, pp. 488-495, 1982

[0015] Compared to spectral hole burning, measuring directly theeye-opening or bit-error rate detection, the advantages of using degreeof polarization as a feedback signal for adaptive polarization modedispersion compensation are:

[0016] 1. independent of bit rate

[0017] 2. applicable to any modulation format without requiringmodifications

[0018] 3. insensitive to chromatic dispersion, such that degree ofpolarization provides a good measure of signal distortion due to onlypolarization mode dispersion

[0019] Depicted in FIG. 2 are as a function of instantaneousdifferential group delay the degree of polarization and Q-penalty of atransmitted signal, non-return to zero (NRZ) format modulated with a bitrate of 48 Gbit/s. The Q-penalty is defined here as: $\begin{matrix}{{Q\text{-}{penalty}} = {{20 \cdot \log}{\frac{{Eye}\text{-}{opening}\quad {of}\quad {received}\quad {signal}}{{Back}\text{-}{to}\text{-}{back}\quad {eye}\text{-}{opening}}.}}} & (1)\end{matrix}$

[0020] For reference, also shown in FIG. 2 is the power of the 24 GHz(half the bit rate) spectral component as a function of instantaneousdifferential group delay. The spectral component at half the bit ratehas been proved to show the strongest dependence on instantaneousdifferential group.

[0021] Contrary to the degree of polarization which shows only onemaximum if the instantaneous differential group delay vanishes, the 24GHz spectral component shows a periodic behaviour. Therefore, in caseswhere the instantaneous differential group delay is expected to exceedon bit duration, at least one more spectral component, namely the 12 GHz(quarter of the bit rate) must be additionally tested to avoid anambiguity.

[0022] The details of degree of polarization and the power of spectralcomponents at 24 GHz (half the bit rate), 12 GHz (quarter of the bitrate) and 6 GHz (eighth the bit rate) are depicted in FIG. 3 for smallvalues of the instantaneous differential group delay.

[0023] Of critical importance in the application of degree ofpolarization as a feedback signal in an adaptive polarization modedispersion compensator, is the accuracy (particularly the variance ofthe measured degree of polarization with the input state ofpolarization) with which the degree of polarization can be measured.

[0024] As can be seen from FIG. 2, if for example a Q-penalty of 0.5 dBmust not be exceeded, the dynamic range of the degree of polarization is±5%. The uncertainty, with which the degree of polarization is measured,must therefore not exceed 5%. An adaptive control algorithm of apolarization mode dispersion compensator needs to sample the degree ofpolarization in the environment of the optimum point in order to trackthe randomly varying differential group delay and principal states ofpolarization. Because of the required sampling by slightly mismatchingthe optical elements with respect to the polarization mode dispersionconditions in the optical fiber, the required accuracy with which thedegree of polarization can be measured is much more stringent.

[0025] A common approach for realizing the required accuracy is tomechanically align the optical components of a polarimeter in adistortion analyzer with high accuracy to predefined angles. However,this is a very tedious and therefore cost intensive way of construction.

SUMMARY OF THE INVENTION

[0026] It is an object of the present invention to provide apolarization mode dispersion compensator based on degree ofpolarization, which does not require a tedious and cost intensive way ofconstruction.

[0027] The polarization mode dispersion compensator according to thepresent invention comprises an optical unit, a distortion analyzer and acontroller. The optical unit receives an input optical signal andoutputs an output optical signal. The distortion analyzer includes apolarimeter, analyzes the output optical signal and produces a feedbacksignal, which represents degree of polarization of the output opticalsignal, by using a polarization property of the polarimeter. Thepolarization property is determined through calibration using intensitysignals output from the polarimeter. The controller produces a controlsignal to adjust the optical unit, based on the feedback signal.

[0028] The optical unit corresponds to adaptive optics and includes oneor more optical elements. the controller corresponds to control logicwhich controls the optical unit using the degree of polarization as afeedback signal. The polarization property of the polarimeter isdetermined in advance to match the actual polarimeter throughcalibration. The distortion analyzer analyzes the output optical signalfrom the optical unit, produces the feedback signal by using theobtained polarization property and outputs it to the controller. Becausethe polarization property is measured after the polarimeter iscompletely assembled, the requirements on mechanical alignment accuracyare drastically relaxed. Tedious, highly-accurate mechanical alignmentis no longer necessary, which can lead to a drastic cost reduction.

BRIEF DESCRIPTION OF THE DRAWINGS

[0029]FIG. 1 shows a configuration of a conventional polarization modedispersion compensator.

[0030]FIG. 2 shows degree of polarization, Q-penalty and a spectralcomponent as a function of instantaneous differential group delay.

[0031]FIG. 3 shows detail of degree of polarization, Q-penalty and aspectral component as a function of instantaneous differential groupdelay.

[0032]FIG. 4 shows a configuration of a distortion analyzer.

[0033]FIG. 5 shows a model of a division of amplitude type polarimeter.

[0034]FIG. 6 shows representation of polarization properties of adivision of amplitude type polarimeter in a Poincaré sphere.

[0035]FIG. 7 shows parameters of the elliptical retarders.

[0036]FIG. 8 shows a setup for calibration of a division of amplitudetype polarimeter.

[0037]FIG. 9 shows a parametric plot of two intensity signals.

[0038]FIG. 10 shows a scaled parametric plot of two intensity signals.

[0039]FIG. 11 shows a location of the first equivalent analyzerpolarization on a Poincaré sphere.

[0040]FIG. 12 shows a circle indicating possible locations of the secondequivalent analyzer polarization on a Poincaré sphere.

[0041]FIG. 13 shows a cross point of circles indicating a possiblelocation of the third equivalent analyzer polarization on a Poincarésphere.

[0042]FIG. 14 shows an orthogonal type configuration of a division ofamplitude type polarimeter.

[0043]FIG. 15 shows equivalent analyzer polarizations of an orthogonaltype configuration on a Poincaré sphere.

[0044]FIG. 16 shows dependence of DOP accuracy on noise and angularuncertainty for an orthogonal type configuration.

[0045]FIG. 17 shows a variant configuration of an orthogonal typepolarimeter.

[0046]FIG. 18 shows a tetragonal type configuration of a division ofamplitude type polarimeter.

[0047]FIG. 19 shows equivalent analyzer polarizations of a tetragonaltype configuration on a Poincaré sphere.

[0048]FIG. 20 shows dependence of DOP accuracy on noise and angularuncertainty for a tetragonal type configuration.

[0049]FIG. 21 shows a variant configuration of a tetragonal typepolarimeter.

[0050]FIG. 22 shows a diamond type configuration of a division ofamplitude type polarimeter.

[0051]FIG. 23 shows equivalent analyzer polarizations of a diamond typeconfiguration on a Poincaré sphere.

[0052]FIG. 24 shows dependence of DOP accuracy on noise and angularuncertainty for a diamond type configuration.

[0053]FIG. 25 shows a variant configuration of a diamond typepolarimeter.

[0054]FIG. 26 shows another variant configuration of a diamond typepolarimeter.

[0055]FIG. 27 shows a variant configuration of a division of amplitudetype polarimeter for autonomous calibration.

[0056]FIG. 28 shows another variant configuration of a division ofamplitude type polarimeter for autonomous calibration.

[0057]FIG. 29 shows a polarization mode dispersion compensator usingdegree of polarization and a state of polarization as feedback signals.

[0058]FIG. 30 shows a polarization mode dispersion compensator usingdegree of polarization and/or a state of polarization and a bit-errorrate as feedback signals.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0059] Hereinafter, preferred embodiments according to the presentinvention will be described in detail by referring to the drawings.

[0060] As a physical property of light, the degree of polarization isused for providing a feedback signal to adjust adaptive optics of apolarization mode dispersion compensator.

[0061] To measure the degree of polarization, an incident beam of lightis split into four or more beams, each of which passes throughindividually arranged retardation and polarizing optics. This type ofpolarization measurement system can be called a division of amplitudetype polarimeter. From the intensities of those beams, the state ofpolarization and the degree of polarization can be calculated if, andonly if, the polarization properties of the paths each beam travels areknown. The accuracy with which the state of polarization and degree ofpolarization can be measured by such an instrument, depends strongly onthe accuracy with which the polarization properties of each path,particularly e.g. polarizer angle, retardance of a path, etc. are known.In the following, an advantageous solution for measuring thepolarization properties with high accuracy of each of the split beams isdescribed.

[0062]FIG. 4 shows an example of the configuration of a distortionanalyzer which measures the degree of polarization and/or the state ofpolarization. The polarimeter 21 splits a light beam into several beamsand outputs intensity signals of those beams. The intensity signals areamplified by the amplifier 22 and converted into digital signals by theanalog-to-digital (A/D) converter 23. The central processing unit (CPU)24 calculates the degree of polarization and/or the state ofpolarization using the values of the digital signals and outputs theobtained result as a feedback signal.

[0063] In the following, various methods will be described to applyingdegree of polarization as a feedback signal to adaptive polarizationmode dispersion compensators. The described methods include advantageousconstruction of polarimeters with respect to degree of polarizationmeasurement accuracy. To relax the stringent requirements on how exactoptical components are aligned, or their orientation is at least known,calibration methods will be described including adapted variations ofpolarimeter constructions.

[0064] As mentioned above, a division of amplitude type polarimeterrefers to a polarimeter in which an incoming light beam is split intoseveral beams. Each beam is then individually guided through opticalcomponents like polarizer (analyzer) and retarder. From the measuredintensities, the state of polarization can be calculated.

[0065] A division of amplitude type polarimeter can be modeled asdepicted in FIG. 5. An incoming light beam {right arrow over (S)} issplit into four beams (more than four beams possible, four beamsselected for description for clarity reasons) by beam splitter 31. Eachof the split beams propagates through a combination of retarder 32 andpolarizer 33 and their respective intensities I₀, I₁, I₂ and I₃, aredetected by photodiodes 34. The retarder/polarizer combinationrepresents an elliptical polarizer, characterized by an azimut θ, anellipticity ε and an extinction ratio ER. The extinction ratio is therelation between the minimum, τ_(min), and maximum, τ_(max), transmittedintensity for all possible input states of polarization. Thepolarization properties each beam experiences while propagating from theinput through the beam splitter 31 until it reaches the polarizer 33,are incorporated in this model by the respective retarder/polarizercombination.

[0066] The relation between the detected intensities I₀, I₁, I₂ and I₃,and the polarization of light at the input of the beam splitter 31(Stokes vector {right arrow over (S)}) can be given as: $\begin{matrix}{{\begin{pmatrix}I_{0} \\I_{1} \\I_{2} \\I_{3}\end{pmatrix} = {Z \cdot \overset{\rightarrow}{S}}},{Z = \begin{pmatrix}\tau_{a0} & {\tau_{d0}\cos \quad 2\theta_{0}\cos \quad 2ɛ_{0}} & {\tau_{d0}\sin \quad 2\theta_{0}\cos \quad 2ɛ_{0}} & {\tau_{d0}\sin \quad 2ɛ_{0}} \\\tau_{a1} & {\tau_{d1}\cos \quad 2\theta_{1}\cos \quad 2ɛ_{1}} & {\tau_{d1}\sin \quad 2\theta_{1}\cos \quad 2ɛ_{1}} & {\tau_{d1}\sin \quad 2ɛ_{1}} \\\tau_{a2} & {\tau_{d2}\cos \quad 2\theta_{2}\cos \quad 2ɛ_{2}} & {\tau_{d2}\sin \quad 2\theta_{2}\cos \quad 2ɛ_{2}} & {\tau_{d2}\sin \quad 2ɛ_{2}} \\\tau_{a3} & {\tau_{d3}\cos \quad 2\theta_{3}\cos \quad 2ɛ_{3}} & {\tau_{d3}\sin \quad 2\theta_{3}\cos \quad 2ɛ_{3}} & {\tau_{d3}\sin \quad 2ɛ_{3}}\end{pmatrix}}} & (2)\end{matrix}$

[0067] The angles θ₀, θ₁, θ₂, θ₃, and ε₀, ε₂, ε₃ describe the ellipticalretarder properties of each retarder/polarizer combination. Thecoefficients τ_(a0), τ_(a1), τ_(a2) and τ_(a3), and τ_(d0), τ_(d1),τ_(d2) and τ_(d3) are related to the minimum, τ_(min), and maximum,τ_(max), transmitted intensity (transmission coefficient) for allpossible input states of polarization by:

τ_(a)=(τ_(max)+τ_(min))/2   (3)

τ_(d)=(τ_(max)−τ_(min))/2   (4)

[0068] Each row of the instrument matrix Z can be thought of in the sameway as a Stokes vector, describing a state of polarization with azimut θand ellipticity ε. Consequently, the retarder/polarizer combination eachbeam passes, can be represented by a point on the Poincaré sphere asdepicted in FIG. 6. The representation in the Poincaré sphere of thepolarization properties each beam experiences, can be called equivalentanalyzer polarization.

[0069] The depicted example of equivalent analyzer polarizations A0, A1,A2 and A3 shows the situation for a division of amplitude typepolarimeter, whereas the parameters of the elliptical retarders(equivalent analyzers) are as shown in FIG. 7.

[0070] In the case the equivalent analyzer polarizations and respectiveextinction ratios are known, the division of amplitude polarimeter isfully characterized with respect to its polarization properties. Theinstrument matrix Z can be calculated and the Stokes vector {right arrowover (S)} at the input of the polarimeter can be calculated from thedetected intensities I₀, I₁, I₂ and I₃ at the photodiodes 34.

[0071] A conventional procedure is to first select values for theequivalent analyzer polarizations and then assembling the opticalcomponents such that their mechanical alignment match the preselectedinstrument matrix. Depending on required accuracy, the alignment must bevery precise. This leads to a tedious and cost intensive assembling.

[0072] A different approach, outlined in the following, provides aprocedure to measure the equivalent analyzer polarizations andrespective extinction ratios with high accuracy. The optical componentscan therefore be assembled with relaxed requirements on alignmentprecision. This leads to an improved performance while at the same timeproviding a way of cost reduction for assembling.

[0073]FIG. 8 shows a setup for autonomous calibration of a division ofamplitude type polarimeter. The calibration procedure starts bymeasuring an assemble of intensity vectors I₀, I₁, I₂ and I₃ fordifferent states of input polarization. The different states of inputpolarization are provided by narrow-bandwidth laser 41 launching fullypolarized light (DOP=100%) into polarization converter 42 withnegligible or at least very low variation of its insertion loss.

[0074] The free-running or by means of external signals controlledpolarization converter 42 launches states of polarization into the, tobe calibrated, division of amplitude polarimeter 43 such that thePoincaré sphere is fully covered.

[0075] In the case the input polarization is modulated in this way, aparametric plot of any two out of the four intensity signals leadsalways to points in a plane surrounded by an ellipse as depicted in FIG.9. The left, right, lower and upper bounds of the ellipse equal theminimum, τ_(min), and maximum, τ_(max), transmission coefficients of therespective analyzers.

[0076] After scaling the intensity signals such that the ellipse fitsinto a square with length of the sides of 1 (multiplication of theintensity signals with factors a and b) as depicted in FIG. 10, theellipticity ε equals, in Poincaré sphere representation, half of theangular spacing ε₀₁ between the two equivalent analyzer polarizationsfor which the parametric plot was drawn. In the following reference,construction of an all-fiber optical in-line and off-line polarizationanalyzer is shown and application of a setup in which a device undertest is placed between in-line and off-line polarimeter to characterizeits polarization transfer function is described. Measurable parametersare polarization dependent loss, retardation, differential group delayand depolarization. Further included applications are fiber-opticalpolarimetric sensors, particularly temperature sensors. Especially,mathematics related to properties of intensity vectors of a division ofamplitude type polarimeter is described on pages 46 through 51.

[0077] “Selbstkalibrierender faseroptischer Polarisationsanalysator”,Jens C. Rasmussen, Ph.D thesis, RWTH Aachen (Germany), Shaker Verlag,ISBN 3-8265-4450-1, 1998

[0078] After the relative angular distances ε₀₁, ε₀₂, ε₀₃, ε₁₂ and ε₁₃between the equivalent analyzer polarizations are known, the absolutepositions are derived as follows.

[0079] The measurement of the degree of polarization is invariant to arotation of the reference frame (rotation of the Poincaré sphere in bothpossible directions) for which the state of polarization is measured.Even for the measurement of the state of polarization itself, a rotationof the reference frame always happens during light propagates through anoptical fiber due to internal and externally introduced birefringence.The absolute orientation of the reference frame (angular orientation ofthe Poincaré sphere) is therefore not important in cases, like here,polarization of light is measured, which has passed through an opticalfiber.

[0080] The first equivalent analyzer polarization A0 can therefore belocated at an arbitrary position on the Poincaré sphere as depicted inFIG. 11. It is fixed here to (azimut, ellipticity)=(0, 0).

[0081] The second equivalent analyzer polarization A1 is located with anangular distance ε₀₁ from the first equivalent analyzer polarization A0on the Poincaré sphere. Possible locations describe therefore a circlearound the first equivalent analyzer polarization A0. Due to thepreviously described rotational invariance, the cross point of thecircle of possible locations and the equator of the Poincaré sphere isselected as depicted in FIG. 12.

[0082] The third equivalent analyzer polarization A2 is located with anangular distance ε₀₂ from the first equivalent analyzer polarization A0,and with an angular distance ε₁₂ from the second equivalent analyzerpolarization A1, on the Poincaré sphere. Possible locations aretherefore the two cross points of the circles around the first andsecond equivalent analyzer polarizations A0 and A1. From those twopossible locations of the third equivalent analyzer polarization A2 onecan be selected as depicted in FIG. 13.

[0083] The fourth equivalent analyzer polarization A3 is located with anangular distance ε₀₃ from the first equivalent analyzer polarization A0,with an angular distance ε₁₃ from the second equivalent analyzerpolarization A1, and with an angular distance ε₂₃ from the thirdequivalent analyzer polarization A2 on the Poincaré sphere. Possiblelocations are therefore the two cross points of the circles around thefirst, second and third equivalent analyzer polarizations A0, A1 and A2.From those possible locations of the fourth equivalent analyzerpolarization A3 one can be selected.

[0084] In the following, the mathematics used to derive the calibrationprocedure is shown. Each analyzer of a division of amplitude typepolarimeter can be described with respect to a common, arbitraryreference plane by an elliptical polarizer. The intensity I_(n)(n=0, 1,2, 3) which can be detected by the n-th analyzer is:

I _(n)=τ_(an)+τ_(dn)(cos 2θ_(n) cos 2ε_(n) S ₁+sin 2θ_(n) cos 2ε_(n) S₂+sin 2ε_(n) S ₃).   (5)

[0085] The polarization in the reference plane is described by theStokes parameters S0, S1, S2 and S3. The equivalent analyzerpolarization of the n-th analyzer is characterized by an azimut θ_(n)and an ellipticity ε_(n). The factors τ_(an) and τ_(dn) can becalculated from the transmission coefficients τ_(maxn)=I_(maxn) andτminn=I_(minn):

τ_(an)=(τ_(maxn)+τ_(minn))/2,   (6)

τ_(dn)=(τ_(maxn)−τ_(minn))/2.   (7)

[0086] Looking at three analyzers which detect the intensities I₀, I₁and I₂, leads to the following equation: $\begin{matrix}\begin{matrix}{{{\overset{\rightarrow}{I}}^{\prime} = {Z^{\prime} \cdot {\overset{\rightarrow}{S}}^{\prime}}},} \\{{{\overset{\rightarrow}{I}}^{\prime} = \begin{pmatrix}{I_{0} - \tau_{a0}} \\{I_{1} - \tau_{a1}} \\{I_{2} - \tau_{a2}}\end{pmatrix}},{{\overset{\rightarrow}{S}}^{\prime} = \begin{pmatrix}S_{1} \\S_{2} \\S_{3}\end{pmatrix}},} \\{Z^{\prime} = {\begin{pmatrix}{\tau_{d0}\cos \quad 2\theta_{0}\cos \quad 2ɛ_{0}} & {\tau_{d0}\sin \quad 2\theta_{0}\cos \quad 2ɛ_{0}} & {\tau_{d0}\sin \quad 2ɛ_{0}} \\{\tau_{d1}\cos \quad 2\theta_{1}\cos \quad 2ɛ_{1}} & {\tau_{d1}\sin \quad 2\theta_{1}\cos \quad 2ɛ_{1}} & {\tau_{d1}\sin \quad 2ɛ_{1}} \\{\tau_{d2}\cos \quad 2\theta_{2}\cos \quad 2ɛ_{2}} & {\tau_{d2}\sin \quad 2\theta_{2}\cos \quad 2ɛ_{2}} & {\tau_{d2}\sin \quad 2ɛ_{2}}\end{pmatrix}.}}\end{matrix} & (8)\end{matrix}$

[0087] Assuming a constant degree of polarization p=(S₁ ²+S₂ ²+S₃²)^(1/2), each state of polarization described by the vector {rightarrow over (S)}′=(S₁, S₂, S₃)^(T) satisfies:

{right arrow over (S)}′ ^(T) ·E·{right arrow over (S)}′=p ²,   (9)

[0088] E: unit matrix.

[0089] This equation describes a sphere in the variables of the vectorcomponents of {right arrow over (S)}′ with a radius p. Combiningequations (8) and (9) leads to: $\begin{matrix}{p^{2} = {{\overset{\rightarrow}{S}}^{\prime \quad T} \cdot E \cdot {\overset{\rightarrow}{S}}^{\prime}}} & (10) \\{\quad {= {\left( {Z^{\prime - 1} \cdot {\overset{\rightarrow}{I}}^{\prime \quad}} \right)^{T} \cdot E \cdot Z^{\prime - 1} \cdot {\overset{\rightarrow}{I}}^{\prime}}}} & (11) \\{\quad {= {\frac{1}{\det \left( Z^{\prime} \right)}{\left( {Z^{\prime \quad T} \cdot {\overset{\rightarrow}{I}}^{\prime}} \right)^{T} \cdot E \cdot \frac{1}{\det \left( Z^{\prime} \right)}}{Z^{\prime \quad T} \cdot {\overset{\rightarrow}{I}}^{\prime}}}}} & (12) \\{\left. \Rightarrow{{\overset{\rightarrow}{I}}^{\prime \quad T} \cdot Z^{\prime} \cdot E \cdot Z^{\prime \quad T} \cdot {\overset{\rightarrow}{I}}^{\prime}} \right. = {{p^{2}\left( {\det \left( Z^{\prime} \right)} \right)}^{2}.}} & (13)\end{matrix}$

[0090] The resultant equation describes a second order plane in thevariables of the components of the vector in three dimensions. A furtherclassification is possible. All eigenvalues of the symmetric matrixZ′·E·Z′^(T) are real and positive. The term p² (det(Z′))² is also alwayspositive. The equation (13) describes therefore an ellipsoid, under theassumption of regularity of the matrix Z′ and all its column vectors arelinear independent. The physical meaning is, that all analyzers arepolarizer (τ_(dn)>0) and the equivalent analyzer polarization are notpairwise identical.

[0091] Normalizing the components of the intensity vector {right arrowover (I)}′, the vectors $\begin{matrix}{\overset{}{I^{''}} = {\begin{pmatrix}{1/\left( {\tau_{\max \quad 0} - \tau_{\min \quad 0}} \right)} & 0 & 0 \\0 & {1/\left( {\tau_{\max \quad 1} - \tau_{\min \quad 1}} \right)} & 0 \\0 & 0 & {1/\left( {\tau_{\max \quad 2} - \tau_{\min \quad 2}} \right)}\end{pmatrix} \cdot \overset{}{I^{\prime}}}} & (14)\end{matrix}$

[0092] describe an ellipsoid, which is inscribed into a cube with thelength of all sides equal to one. The possible values for each componentof the intensity vector {right arrow over (I)}″ is now limited to−0.5<I_(n)″<0.5. The first analyzer detects a maximum intensity I₀″=0.5if the polarization in the reference plane equals the equivalentanalyzer polarization. For the first analyzer, the detected intensityI₀″: $\begin{matrix}{I_{0}^{''} = {0.5\quad {therefore}\quad {maximum}\quad {for}\left\{ {\begin{matrix}{S_{1} = {\cos \quad 2\theta_{1}\cos \quad 2ɛ_{1}}} \\{S_{2} = {\cos \quad 2\theta_{1}\cos \quad 2ɛ_{1}}} \\{S_{3} = {\sin \quad 2ɛ_{1}}}\end{matrix}.} \right.}} & (15)\end{matrix}$

[0093] The second analyzer detects at the same polarization at which thefirst analyzer detect the maximum intensity, an intensity I₁″ with:$\begin{matrix}\begin{matrix}{{2{I_{1}^{''}\left( {I_{0}^{''} = 0.5} \right)}} = {{\cos \quad 2\theta_{0}\cos \quad 2ɛ_{0}\cos \quad 2\theta_{1}\cos \quad 2ɛ_{1}} +}} \\{{{\sin \quad 2\theta_{0}\cos \quad 2ɛ_{0}\sin \quad 2\quad \theta_{1}\cos \quad 2ɛ_{1}} +}} \\{{\sin \quad 2ɛ_{0}\sin \quad 2{ɛ_{1}.}}}\end{matrix} & (16)\end{matrix}$

[0094] The right side of equation (16) is equal to the cosine of theangle ∠{overscore (P)}_(Ana0){overscore (P)}_(Ana1) between theequivalent analyzer polarizations of the first {overscore (P)}_(Ana0)and second {overscore (P)}_(Ana1) analyzer, because $\begin{matrix}{{\cos \left( {\angle \quad {\overset{}{P}}_{Ana0}{\overset{}{P}}_{Ana1}} \right)} = {\frac{{\overset{}{P}}_{Ana0}{\overset{}{P}}_{Ana1}}{{{\overset{}{P}}_{Ana0}} \cdot {{\overset{}{P}}_{Ana1}}}.}} & (17)\end{matrix}$

[0095] The orthogonal projection of the ellipsoid composed of thevectors {overscore (I)}″ on the coordinate plane I₀″, I₁″ leads to aplane with an elliptical shape. For the length of the main axis a and band the ellipticity ε of the elliptically shaped plane and for the valueI₁″(I₀″_(max)), the following relations apply: $\begin{matrix}{{{\tan \quad ɛ} = \frac{b}{a}},} & (18)\end{matrix}$

 cos δ=2I ₁″(I ₀″_(max)),   (19) $\begin{matrix}{{\left. \begin{matrix}{{a^{2} + b^{2}} = \frac{1}{2}} \\{{\pm {ab}} = {\frac{1}{4}\sin \quad \delta}}\end{matrix} \right\} {Lemma}\quad {of}\quad {{Apollonius}.}}\quad} & (20)\end{matrix}$

[0096] From this, the relation of the angle between the equivalentanalyzer polarizations {right arrow over (P)}_(Ana0), {right arrow over(P)}_(Ana1) and the ellipticity ε can be derived. From equations(18)-(20): $\begin{matrix}\begin{matrix}{\frac{2\quad a\quad b}{a^{2} + b^{2}} = {{\pm \sin}\quad \delta}} \\{= \frac{2\quad \tan \quad ɛ}{1 + {\tan^{2}ɛ}}} \\{= {\sin \quad 2ɛ}} \\{\left. \Rightarrow\quad \delta \right. = {{\pm 2}\quad {ɛ.}}}\end{matrix} & (21)\end{matrix}$

[0097] With equations (16), (17) and (19) the relation of the angle∠{right arrow over (P)}_(Anan){right arrow over (P)}_(Anam) between twoequivalent analyzer polarizations {right arrow over (P)}_(Anan), {rightarrow over (P)}_(Anam) and the ellipticity ε_(nm) calculates to:

cos (∠{right arrow over (P)} _(Anan){right arrow over (P)}_(Anam))=2I″_(m)(I _(n)″_(max))=cos δ_(nm)=cos 2ε_(nm)   (22)

∠{right arrow over (P)}_(Anan){right arrow over (P)}_(Anam)=2ε_(nm).  (23)

[0098] This applies to each possible pair of analyzers.

[0099] Next, with respect to the principle measurement accuracy of thedegree of polarization, three configurations and possible variations ofa division of amplitude type polarimeter are discussed. Thoseconfigurations are named “Orthogonal”, “Tetragonal” and “Diamond”. Theydiffer in the number and arrangement of utilized optical components. The“Orthogonal” scheme is used in the following reference.

[0100] “A study for wavelength dependency of Polarization AnalysisModule”, T. Miyakoshi, S. Shikii, Y. Hotta, S. Boku, Institute ofElectronics, Information and Communication Engineers, sougou taikaiB-10-95, p. 528, 2001

[0101] In this reference, a division of amplitude type polarimeter,composed of three beam-splitters, four polarizers, one quarter-waveretarder, four photodiodes and data acquisition electronics aredescribed.

[0102] “Tetragonal” is a compromise between complexity and realizableaccuracy. “Diamond” is with respect to DOP accuracy and sensitivity tonoise an ideal configuration but requires the most complex arrangement.

[0103] To compare the principal performance of a specific arrangement,the condition number of the 4×4 instrument matrix, describing therelation between measured optical intensities and the Stokes vector, canbe used. The condition numbers (calculated according to Hadamard) of theschemes “Orthogonal”, “Tetragonal” and “Diamond” are 2.0, 1.5 and 1.3,respectively.

[0104] In order to numerically investigate the dependence of theprincipal DOP accuracy on angular misalignment of optical components,the difference between real and supposed polarizer angles has beenvaried through the values 0°, 0.1°, 0.5°, 1° up to 2°. Those valueswhere alternatively added to and subtracted from the four polarizerangles, which can be supposed to be approximately the worst case.

[0105] To take further into account noise, the quantification noise dueto A/D conversion of the photodiode currents is supposed to be the mainsource. The resolution of A/D conversion has been varied through thevalues 8, 10, 12, 14 up to 16 bit.

[0106] The offsets due to photodiode dark currents and amplifiers aresupposed to be zero. Signals are supposed to fully cover the dynamicrange of the A/D conversion. Extinction ratios of the polarizers aresupposed to be arbitrary high. Incorporated retardations are supposed tobe fixed.

[0107] An “Orthogonal” type configuration of a division of amplitudetype polarimeter is depicted in FIG. 14. A basic configuration of thispolarimeter includes three beam splitters 51, 52 and 53, four polarizers54, 55, 56 and 57, and one retarder 58 with retardation of a quarter ofa wavelength. Angles of the polarizers 54 and 57 are 0° and angles ofthe polarizers 55 and 56 are 45° and −45°, respectively. As shown inFIG. 15, the components are arranged such that the equivalent analyzerpolarizations (A0, A1, A2, A3) are mutually orthogonal on a Poincarésphere. The dependence of the principal DOP accuracy [%] on noise (A/Dresolution [bit]) and angular uncertainty [°] is shown for exemplifiedvalues in FIG. 16.

[0108] A variant configuration of the “Orthogonal” type polarimeter isdepicted in FIG. 17. This polarimeter includes three beam splitters 61,62 and 63, four polarizers 64, 65, 66 and 67, and one retarder 68 withretardation of a quarter of a wavelength. Angles of the polarizers 64and 65 are 0° and angles of the polarizers 66 and 67 are 45° and −45°,respectively.

[0109] A “Tetragonal” type configuration of a division of amplitude typepolarimeter is depicted in FIG. 18. A basic configuration of thispolarimeter includes three beam splitters 71, 72 and 73, four polarizers74, 75, 76 and 77, and one retarder 78 with retardation of a quarter ofa wavelength. Angles of the polarizers 74 and 77 are 0° and angles ofthe polarizers 75 and 76 are 60° and −60°, respectively. As shown inFIG. 19, the components are arranged such that the equivalent analyzerpolarizations (A0, A1, A2, A3) are angular spaced by 120° on a Poincarésphere. A3 is orthogonal to all other equivalent analyzer polarizations.The dependence of the principal DOP accuracy on noise and angularuncertainty is shown for exemplified values in FIG. 20.

[0110] A variant configuration of the “Tetragonal” type polarimeter isdepicted in FIG. 21. This polarimeter includes three beam splitters 81,82 and 83, four polarizers 84, 85, 86 and 87, and one retarder 88 withretardation of a quarter of a wavelength. Angles of the polarizers 84and 85 are 0° and angles of the polarizers 86 and 87 are 60° and −60°,respectively.

[0111] A “Diamond” type configuration of a division of amplitude typepolarimeter is depicted in FIG. 22. A basic configuration of thispolarimeter includes three beam splitters 91, 92 and 93, four polarizers94, 95, 96 and 97, and four retarders 98, 99, 100 and 101. Angles of thepolarizers 94 and 97 are 0° and angles of the polarizers 95 and 96 are60° and −60°, respectively. Retardation of the retarders 98, 99 and 100is {fraction (1/18.48)} of a wavelength and that of the retarder 101 isa quarter of a wavelength. As shown in FIG. 23, the components arearranged such that the equivalent analyzer polarizations (A0, A1, A2,A3) form a structure like atoms in a diamond on a Poincaré sphere. Thedependence of the principal DOP accuracy on noise and angularuncertainty is shown for exemplified values in FIG. 24.

[0112] A variant configuration of the “Diamond” type polarimeter isdepicted in FIG. 25. This polarimeter includes three beam splitters 111,112 and 113, four polarizers 114, 115, 116 and 117, and four retarders118, 119, 120 and 121. Angles of the polarizers 114 and 115 are 0° andangles of the polarizers 116 and 117 are 60° and −60°, respectively.Retardation of the retarder 118 is a quarter of a wavelength and that ofthe retarders 119, 120 and 121 is {fraction (1/18.48)} of a wavelength.

[0113]FIG. 26 shows another variant configuration of the “Diamond” typepolarimeter. This polarimeter includes three beam splitters 131, 132 and133, four polarizers 134, 135, 136 and 137, and two retarders 138 and139. Angles of the polarizers 134 and 135 are 0° and angles of thepolarizers 136 and 137 are 60° and −60°, respectively. Retardation ofthe retarder 138 is {fraction (1/18.48)} subtracted from a quarter of awavelength and that of the retarder 139 is {fraction (1/18.48)} of awavelength.

[0114] In the above described configurations, the angles of thepolarizers and the retardation of the retarders are not limited to therespective theoretical values themselves but can be within a giventolerance range (±5% for example) of the values.

[0115] The autonomous calibration procedure requires besides a constantdegree of polarization of the light source, which is easy to realize, aconstant input power. This can be realized by either using polarizationconverters for polarization modulation with low dependence of theinsertion loss on polarization like crystal based or fiber baseddevices. In the case a polarization converter with untolerable highdependence of insertion loss on polarization is used, like multi stagesof variable birefringent plates or integrated optical realizations, thepower of the light wave must be measured simultaneous with theintensities of the polarimeter to be calibrated.

[0116] Simultaneous power measurement can be either realized by a 1×2coupler, whereas one arm is used for power monitoring and the other forthe polarimeter to be calibrated.

[0117] An alternative is to realize a division of amplitude typepolarimeter where only three polarizers are used and one of the fourlight beams is used for the power monitoring as depicted in FIG. 27. Theconfiguration shown in FIG. 27 is obtained by removing the polarizer 67from the configuration shown in FIG. 17.

[0118] Another realization possibility is depicted in FIG. 28, in whichthe light beam is split into five beams. The configuration shown in FIG.28 is obtained by inserting an additional beam splitter 140 into theconfiguration shown in FIG. 26. While four of the beams are transmittedthrough optics as described above, the fifth beam from the beam splitter140 is used for power monitoring.

[0119] In the application of a division of amplitude type polarimeterfor an adaptive polarization mode dispersion compensator as a distortionmonitor, one of the described variants can be used, whereas the requiredaccuracy for the degree of polarization measurement is provided afterthe described calibration procedure (measurement of the instrumentmatrix Z) has been applied. The basic algorithm for adjusting theadaptive optics of a polarization mode dispersion compensator, isprovided by means of a gradient search algorithm assuring a maximumdegree of polarization.

[0120] In order to improve the speed with which the adaptive optics of apolarization mode dispersion compensator can be controlled and/or toavoid ambiguities of the correlation between degree of polarization andsignal distortion due to polarization mode dispersion, in the followingother variants are described.

[0121] While it is possible to adaptively control a polarization modedispersion compensator by tracking the maximum degree of polarization,the principal realizable tracking speed could be improved by includingthe measured state of polarization. In general, the measured state ofpolarization is very sensitive to variations of the polarizationtransfer function of an optical fiber, while the degree of polarizationshows only moderate sensitivity which can be covered by the limitedmeasurement accuracy even if it is in the order of 1% or better.

[0122] Monitoring beside the degree of polarization also the state ofpolarization as depicted in FIG. 29 leads to the possibility of a moresophisticated algorithm. The polarization mode dispersion compensatorshown in FIG. 29 includes adaptive optics 141, distortion analyzer 142and control logic 143. The distortion analyzer 142 provides beside thedegree of polarization as a measure of signal distortion also the stateof polarization to the control logic 143 as feedback signals. Thecontrol logic 143 receives the feedback signals and produces a controlsignal for the adaptive optics 141 based on the received signals.

[0123] As long as the state of polarization shows only small variations,the polarization mode dispersion properties of the optical transmissionsystem also only vary slightly and readjustment of the adaptive optics141 is not required during this time. This idle time can beadvantageously used to perform other operations like readjusting orrewinding components of a polarization converter to their main operatingpoint.

[0124] In the case the state of polarization changes, the polarizationmode dispersion properties of the optical transmission system havechanged and readjustment of the adaptive optics 141 is necessary. Theangular change and speed with which the state of polarization haschanged, can be used as a measure of how strong the conditions of theadaptive optics 141 must be readjusted.

[0125] To avoid ambiguities, i.e. cases in which a maximum degree ofpolarization does not correspond to minimum signal distortion, acombination of degree of polarization as a fast feedback signal, and abit-error rate as provided by e.g. forward-error-correcting electronicsas an ultimate measure of signal distortion can be used as depicted inFIG. 30. The polarization mode dispersion compensator shown in FIG. 30has a similar configuration to that shown in FIG. 29. The distortionanalyzer 142 provides the control logic 143 with only the degree ofpolarization or the combination of the degree of polarization and thestate of polarization. Receiver 144 includes forward-error-correctingelectronics and outputs a bit-error rate as a feedback signal. Thecontrol logic 143 receives the feedback signals from the distortionanalyzer 142 and the receiver 144 and produces a control signal for theadaptive optics 141 based on the received signals.

[0126] While fast changes of the polarization mode dispersion propertiesof an optical transmission system require a fast feedback signal asprovided by the measurement of the degree of polarization, for finetuning purposes the bit-error rate as provided by theforward-error-correcting electronics at the receiver 144 is used.

[0127] As described in detail above, according to the present invention,the requirements on mechanical alignment accuracy for a polarimeter aredrastically relaxed since the polarization properties are measured afterthe polarimeter is assembled. Therefore, tedious and cost intensivemechanical alignment is not required.

What is claimed is:
 1. A polarization mode dispersion compensatorcomprising: an optical unit receiving an input optical signal andoutputting an output optical signal; a distortion analyzer whichincludes a polarimeter, analyzing the output optical signal andproducing a feedback signal, which represents degree of polarization ofthe output optical signal, by using a polarization property of thepolarimeter, the polarization property determined through calibrationusing a plurality of intensity signals output from the polarimeter; anda controller producing a control signal to adjust said optical unit,based on the feedback signal.
 2. A polarization mode dispersioncompensator according to claim 1, wherein: said polarimeter includes aplurality of optical components to produce the intensity signals; saiddistortion analyzer produces the feedback signal by using information ofan instrument matrix of the polarimeter as the polarization property;and the information of the instrument matrix is obtained by inputtinglight with different states of polarization into the polarimeter suchthat a Poincaré sphere is fully covered and measuring the intensitysignals output from the polarimeter.
 3. A polarization mode dispersioncompensator according to claim 2, wherein the information of theinstrument matrix is obtained by plotting two of the intensity signalson a plane for the different states of polarization and determining anazimut and an ellipticity of an ellipse which surrounds plotted points.4. A polarization mode dispersion compensator according to claim 3,wherein maximum and minimum intensity of the plotted points are furtherdetermined for each of the two of the intensity signals and used,together with the azimut and ellipticity, as the information of theinstrument matrix.
 5. A polarization mode dispersion compensatoraccording to claim 1, wherein: said polarimeter includes a plurality ofoptical components forming four analyzers to produce four intensitysignals; and the optical components are arranged such that equivalentanalyzer polarizations of three of the four analyzers are angular spacedby 120 degrees on a Poincaré sphere and an equivalent analyzerpolarization of another of the four analyzers is orthogonal to theequivalent analyzer polarizations of the three analyzers on the Poincarésphere.
 6. A polarization mode dispersion compensator according to claim1, wherein: said polarimeter includes a plurality of optical componentsforming four analyzers to produce four intensity signals; and theoptical components are arranged such that equivalent analyzerpolarizations of the four analyzers form a structure like atoms in adiamond on a Poincaré sphere.
 7. A polarization mode dispersioncompensator according to claim 1, wherein: said distortion analyzerproduces a feedback signal which represents a state of polarization ofthe output optical signal; and said controller produces the controlsignal based on both the feedback signal representing the degree ofpolarization and the feedback signal representing the state ofpolarization.
 8. A polarization mode dispersion compensator according toclaim 1, wherein said controller receives a feedback signal whichrepresents a bit-error rate of the output optical signal and producesthe control signal based on both the feedback signal representing thedegree of polarization and the feedback signal representing thebit-error rate.
 9. A polarization mode dispersion compensator accordingto claim 1, wherein: said distortion analyzer produces a feedback signalwhich represents a state of polarization of the output optical signal;and said controller receives a feedback signal which represents abit-error rate of the output optical signal and produces the controlsignal based on the feedback signal representing the degree ofpolarization, the feedback signal representing the state of polarizationand the feedback signal representing the bit-error rate.
 10. Adistortion analyzer comprising: a polarimeter which includes a pluralityof optical components to produce a plurality of intensity signals froman input optical signal; and a processor producing a feedback signal,which represents degree of polarization of the input optical signal, forpolarization mode dispersion compensation from the intensity signals byusing a polarization property of the polarimeter, the polarizationproperty determined through calibration using intensity signals outputfrom the polarimeter.
 11. A polarimeter comprising: three beamsplitters; two polarizers within a given tolerance range of zerodegrees; a polarizer within a given tolerance range of 60 degrees; apolarizer within a given tolerance range of −60 degrees; and a retarderwithin a given tolerance range of a quarter of a wavelength, wherein thebeam splitters, the polarizers and the retarder form four analyzers toproduce four intensity signals, and are arranged such that equivalentanalyzer polarizations of three of the four analyzers are angular spacedby 120 degrees on a Poincaré sphere and an equivalent analyzerpolarization of another of the four analyzers is orthogonal to theequivalent analyzer polarizations of the three analyzers on the Poincarésphere.
 12. A polarimeter comprising: three beam splitters; twopolarizers within a given tolerance range of zero degrees; a polarizerwithin a given tolerance range of 60 degrees; a polarizer within a giventolerance range of −60 degrees; a retarder within a given tolerancerange of a quarter of a wavelength; and three retarders within a giventolerance range of {fraction (1/18.48)} of a wavelength, wherein thebeam splitters, the polarizers and the retarders form four analyzers toproduce four intensity signals, and are arranged such that equivalentanalyzer polarizations of the four analyzers form a structure like atomsin a diamond on a Poincaré sphere.
 13. A polarimeter comprising: threebeam splitters; two polarizers within a given tolerance range of zerodegrees; a polarizer within a given tolerance range of 60 degrees; apolarizer within a given tolerance range of −60 degrees; a retarderwithin a given tolerance range of {fraction (1/18.48)} subtracted from aquarter of a wavelength; and a retarder within a given tolerance rangeof {fraction (1/18.48)} of a wavelength, wherein the beam splitters, thepolarizers and the retarders form four analyzers to produce fourintensity signals, and are arranged such that equivalent analyzerpolarizations of the four analyzers form a structure like atoms in adiamond on a Poincaré sphere.
 14. A method of polarization modedispersion compensation, comprising: determining a polarization propertyof a polarimeter through calibration using a plurality of intensitysignals output from a polarimeter; producing an output optical signalthrough an optical unit from an input optical signal; analyzing theoutput optical signal and producing a feedback signal, which representsdegree of polarization of the output optical signal, by using thepolarization property of the polarimeter; and adjusting said opticalunit according to the feedback signal.
 15. A polarization modedispersion compensator comprising: optical means for receiving an inputoptical signal and outputting an output optical signal; distortionanalyzer means which includes polarimeter means, for analyzing theoutput optical signal and producing a feedback signal, which representsdegree of polarization of the output optical signal, by using apolarization property of the polarimeter means, the polarizationproperty determined through calibration using a plurality of intensitysignals output from the polarimeter means; and controller means forproducing a control signal to adjust said optical means, based on thefeedback signal.
 16. A distortion analyzer comprising: polarimeter meanswhich includes a plurality of optical means to produce a plurality ofintensity signals from an input optical signal; and processor means forproducing a feedback signal, which represents degree of polarization ofthe input optical signal, for polarization mode dispersion compensationfrom the intensity signals by using a polarization property of thepolarimeter means, the polarization property determined throughcalibration using intensity signals output from the polarimeter means.